Erick - I think there should be a rule that to discuss a book one must read the book
1. Nakai and Tsuboi did not do Yagyu Shinkage-ryu - they did Yagyu Shingan-ryu. Different ryu entirely. Different documents. Different esoteric training. Different physical training. Sort of like the Carribean pirates and the Pittsburgh Pirates. Or maybe that the fact that Joseph Smith was a Mormon proves that Will Smith, the actor sings in the Mormon Tabernacle Choir.
2. I explained in the book in considerable detail that Ueshiba DID study Yagyu Shinkage-ryu, in a fashion from Kisaburo Gejo and noted, as does Josh the kata that he taught, in his fashion at Shingu, and that Tomiki Kenji also said so. That is nothing new to the discussion.
3. The debate here is (well, should be) what the nature of a menkyo that Takeda gave Ueshiba. And whether, in some fashion, despite a dearth of any other evidence, either documentary or more important physically (in the sword of Takeda), that HE somehow did Yagyu Shinkage-ryu. The lineage in the menkyo, alone, establishes to my satisfaction that Takeda did not - but rather like Ueshiba, he felt that he could look at anything and say, "In aiki, we do it this way."
Ellis Amdur